Covariance structures play a fundamental role in high-dimensional statistics. It is of direct interest in a wide range of applications including genomic data analysis, particularly for hypothesis generation. Knowledge of the covariance structure is critical to many statistical methods, including discriminant analysis, principal component analysis, clustering analysis, and regression analysis. In the high-dimensional setting with complete data, inference on the covariance structure has been actively studied in recent years. See Cai, Ren and Zhou [1]} for a survey of recent results on minimax and adaptive estimation of high-dimensional covariance and precision matrices under various structural assumptions.
Estimation of high-dimensional covariance matrices in the presence of missing data also has wide applications in biomedical studies, particularly in integrative genomic analysis which holds great potential in providing a global view of genome function (see Hawkins et al. [2]}).
